H∞ Synthesis for a Planar Flexible Cable-Driven Robot

Abstract

This paper presents the modeling and control of a flexible cable-driven parallel robot, taking into account the flexibility of the cables. The model is obtained based on the Lagrangian method and the assumed modes approach. Considering three cables, this model has been formulated using differential-algebraic equations and then transformed into an ordinary differential equations representation. Based on the linearization of the ODE representation along the center of the work-space, an ${\mathcal{H}_\infty }$ controller guaranteeing disturbance rejection and reference tracking has been synthesized. A reduced-order version of this controller has been also obtained. Our simulation results performed with the non-linear model show the good performance of the closed-loop system. A comparison between the reduced-order ${\mathcal{H}_\infty }$ controller and a PD controller taken from the literature has also been provided.